00:01
Hello, so here we want the equation of a line.
00:04
We'll pass to the point 0 .03.
00:05
It has slope 2 over x plus 1 at any point xy.
00:09
While if the slope is always 2x plus 1, that means that's the derivative.
00:13
So to find the function, we just integrate 2 over x plus 1.
00:16
So we take the integral of 2 over x plus 1 d x.
00:22
We can do a u substitution here if we let u be equal to well x plus 1, then the derivative of u, du is equal to just while the derivative of x is just 1 plus 0.
00:37
So the derivative of du here is going to be equal to just the x.
00:42
So we can do a substitution and we can bring out the 2 in front here.
00:48
It's going to be equal to 2 times the integral of just 1 over u, du.
00:54
And while the integral of 1 over u, du is a natural log of the absolute value of u...